Advertisements
Advertisements
Question
The electric field at a point associated with a light wave is `E = (100 "Vm"^-1) sin [(3.0 xx 10^15 "s"^-1)t] sin [(6.0 xx 10^15 "s"^-1)t]`.If this light falls on a metal surface with a work function of 2.0 eV, what will be the maximum kinetic energy of the photoelectrons?
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
Advertisements
Solution
Given :-
`E = 100 sin [(3 xx 10^-15 "s"^-1)t] sin [(6 xx 10^-15 "s"^-1)t]`
= `100 xx 1/2 cos [(9 xx 10^15 "s"^-1)t] - cos[(3 xx 10^15 "s"^-1)t]`
The values of angular frequency `ω` are `9 xx 10^15` and `3 xx 10^15`.
Work function of the metal surface, `phi = 2 "eV"`
Maximum frequency,
`v = ω_(max)/(2pi) = (9 xx 10^15)/(2pi) Hz`
From Einstein's photoelectric equation, kinetic energy,
K = hv - `phi`
`⇒ K = 6.63 xx 10^-34 xx (9 xx 10^15)/(2pi) xx 1/(1.6 xx 10^-19) - 2 "eV"`
⇒ K = 3.938 eV
APPEARS IN
RELATED QUESTIONS
In an experiment on the photoelectric effect, the slope of the cut-off voltage versus the frequency of incident light is found to be 4.12 × 10−15 Vs. Calculate the value of Planck’s constant.
The work function for a certain metal is 4.2 eV. Will this metal give photoelectric emission for incident radiation of wavelength 330 nm?
Light of wavelength 488 nm is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) potential of photoelectrons is 0.38 V. Find the work function of the material from which the emitter is made.
In an accelerator experiment on high-energy collisions of electrons with positrons, a certain event is interpreted as annihilation of an electron-positron pair of total energy 10.2 BeV into two γ-rays of equal energy. What is the wavelength associated with each γ-ray? (1BeV = 109 eV)
Write Einstein’s photoelectric equation?
Briefly explain the three observed features which can be explained by Einstein’s photoelectric equation.
A non-monochromatic light is used in an experiment on photoelectric effect. The stopping potential
A monochromatic light source of intensity 5 mW emits 8 × 1015 photons per second. This light ejects photoelectrons from a metal surface. The stopping potential for this setup is 2.0 V. Calculate the work function of the metal.
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
Consider the situation of the previous problem. Consider the faster electron emitted parallel to the large metal plate. Find the displacement of this electron parallel to its initial velocity before it strikes the large metal plate.
(Use h = 6.63 × 10-34J-s = 4.14 × 10-15 eV-s, c = 3 × 108 m/s and me = 9.1 × 10-31kg)
How does one explain the emission of electrons from a photosensitive surface with the help of Einstein’s photoelectric equation?
Use Einstein's photoelectric equation to show how from this graph,
(i) Threshold frequency, and
(ii) Planck's constant can be determined.
According to Einstein's photoelectric equation, the plot of the kinetic energy of the emitted photoelectrons from a metal versus the frequency of the incident radiation gives a straight line, whose slope ______.
Each photon has the same speed but different ______.
The minimum energy required to remove an electron is called ______.
A student performs an experiment on photoelectric effect, using two materials A and B. A plot of Vstop vs ν is given in Figure.
- Which material A or B has a higher work function?
- Given the electric charge of an electron = 1.6 × 10–19 C, find the value of h obtained from the experiment for both A and B.
Comment on whether it is consistent with Einstein’s theory:
Radiation of frequency 1015 Hz is incident on three photosensitive surfaces A, B and C. Following observations are recorded:
Surface A: no photoemission occurs
Surface B: photoemission occurs but the photoelectrons have zero kinetic energy.
Surface C: photo emission occurs and photoelectrons have some kinetic energy.
Using Einstein’s photo-electric equation, explain the three observations.
The photon emitted during the de-excitation from the first excited level to the ground state of a hydrogen atom is used to irradiate a photocathode in which the stopping potential is 5 V. Calculate the work function of the cathode used.
If c is the velocity of light in free space, the correct statements about photon among the following are:
- The energy of a photon is E = hv.
- The velocity of a photon is c.
- The momentum of a photon, ρ = `(h v)/c`.
- In a photon-electron collision, both total energy and total momentum are conserved.
- Photon possesses positive charge.
Choose the correct answer from the options given below:
